Experimental Mathematics
- Experiment. Math.
- Volume 10, Issue 1 (2001), 25-34.
Central binomial sums, multiple Clausen values, and zeta values
Jonathan Michael Borwein, David J. Broadhurst, and Joel Kamnitzer
Abstract
We find and prove relationships between Riemann zeta values and central binomial sums. We also investigate alternating binomial sums (also called Apery sums). The study of nonalternating sums leads to an investigation of different types of sums which we call multiple Clausen values. The study of alternating sums leads to a tower of experimental results involving polylogarithms in the golden ratio.
Article information
Source
Experiment. Math., Volume 10, Issue 1 (2001), 25-34.
Dates
First available in Project Euclid: 30 August 2001
Permanent link to this document
https://projecteuclid.org/euclid.em/999188418
Mathematical Reviews number (MathSciNet)
MR1 821 569
Zentralblatt MATH identifier
0998.11045
Subjects
Primary: 11Mxx: Zeta and $L$-functions: analytic theory
Secondary: 05Axx: Enumerative combinatorics {For enumeration in graph theory, see 05C30} 11Bxx: Sequences and sets 33Bxx: Elementary classical functions
Keywords
binomial sums multiple zeta values log-sine integrals Clausen's function multiple Clausen values polylogarithms Apéry sums
Citation
Borwein, Jonathan Michael; Broadhurst, David J.; Kamnitzer, Joel. Central binomial sums, multiple Clausen values, and zeta values. Experiment. Math. 10 (2001), no. 1, 25--34. https://projecteuclid.org/euclid.em/999188418
